In the context of the rapid dissemination of multimedia content, identifying disinformation on social media platforms such as TikTok represents a significant challenge. This study introduces a hybrid framework that combines the computational power of deep learning with the interpretability of fuzzy logic to detect suspected disinformation in TikTok videos. The methodology is comprised of two core components: a multimodal feature analyser that extracts and evaluates data from text, audio, and video; and a multimodal disinformation detector based on fuzzy logic. These systems operate in conjunction to evaluate the suspicion of spreading disinformation, drawing on human behavioural cues such as body language, speech patterns, and text coherence. Two experiments were conducted: one focusing on context-specific disinformation and the other on the scalability of the model across broader topics. For each video evaluated, high-quality, comprehensive, well-structured reports are generated, providing a detailed view of the disinformation behaviours.

Weaknesses: The proof, as described by the authors themselves, depend on the assumption on the gap optimality. The relationship between the approximation error and this optimality gap is crucial, a larger approximation error requires a larger gap to ensure the favorable properties. It is not entirely clear whether these bounds are meaningful in practice. Secondly, the algorithm for the general case requires an oracle to determine the most uncertain action given a state for the approximation family F. While it is argued that a similar oracle is used in previous work, it is not clear whether this is more realistic than previous work dismissed by the authors in related work ("Know-What-It-Knows" oracle in Li et al. 2011). The proof applies only to deterministic systems, restricting its application significantly.

This paper makes progress on our theoretical understanding of function approximation in RL, a crucial and tricky topic. The paper is technically strong and proposes a highly novel recursion-based algorithm that could open the door to future innovations.

Additional Feedback: page 1, last para: this is confusing to read. The reference cited here is Babai's paper. Why is the slowness of current graph isomorphism algorithms relevant to the problem of producing isomorphism-injective graph representations? Definition 3: a minor point, but it is useful to say what is meant by size (e.g., #edges, or size of description of the graph) After definition 7, it is useful to formally define the notion of "universal function approximator", as this could be interpreted in different ways The notation of multi-function in Definition 6 uses a double arrow, but it doesn't seem to get used consistently like that. It is used with a single arrow in Definition 7. Also the notion is confusing, since it is not a function into the range but into its power set.

Each reviewer believes that the paper is poorly written. The reviewers, though, have agreed that (i) the problem is interesting, that (ii) the theoretical results seem to hold, and that (iii) they are interesting. On the other hand, it is not clear whether a quick revision would solve all or many of the readability issues.

Weaknesses: - While the theoretical results seem correct, it is not clear to me the advantages of this approach compared to previous work, in particular, gradient Q-learning (GQ). On line 110, it is written that the assumptions are not as stringent but I am not convinced that this is the case. Could the authors clarify this point? If I am interpreting it correctly, it assumes that we have a fixed replay buffer of data on which we are doing updates, as in the offline batch RL setting. It is not specified which policy is used to collect this data and I would expect certain assumptions on this behavior policy.

This paper presents a new objective and an algorithm, which is similar to DQN, that optimises for that objective. Similar to prior work (GTD, TDC, GQ), the algorithm is shown to be convergent under linear function approximation. Because the objective is different, the paper could have better illustrated what this means in terms of the quality of the fixed point the new algorithm converges to - this is only discussed in detail in a special case of a diagonal feature covariance matrix. The author response did not lift this concern, and it remains unclear whether the new algorithm has major benefits over existing related work. The experiments were deemed somewhat insufficient to fully convince the reviewers of this.

Additional Feedback: After rebuttal: I read the author response and other reviews. It would be great to see more discussions in the next version. I think this paper has enough contribution and I will keep my original rating for acceptance. This paper is well written, and easy to follow. The main text is clean and the proof is deferred to the appendix.

All reviewers agree that the paper makes a nice contribution to planning with function approximation. In particular, the paper considers an important open problem, and while the problem is solved by making a few assumptions (mostly notably the core states), the results have made significant progress on the important problem. The reviewers also appreciate the use of precise language and careful description of related work. Among the remaining concerns, R2 wants to see some evidence of robustness against the failure of the "core state" assumption. While performing empirical experiments may not fit the theoretical nature of the paper, the authors can consider a theoretical justification: namely, define a notion of error that measures how much the core-states assumption is violated, and show how such an error manifest itself in the final guarantee.

I would just like to confirm my understanding of the algorithmic contributions of this work. As far as I understand, Jin et al [2019] propose a learning algorithm for the standard RL case with linear function approximation in linear MDPs. Then Jin et al [2020] propose a method for efficient exploration in the reward-free RL case. This is for normal MDPs but in the tabular setting. In that work, exploration is achieved by constructing a reward function where the reward is 1 for states that are "significant", and 0 otherwise, and then solving the resulting task with an efficient learning algorithm.